12. A pendulum bob is released from rest at position X which is at a height h above its lowest position Y and then passes through position Z. Position Z is 0.4h above Y. Assuming air resistance is negligible, ﬁnd the ratio of the speed of the bob at position Y to that at position Z.
By Principle of conservation of energy, the energy at points X, Y and Z are all the same. This means that we can express the speeds at Y and Z in terms of the gravitational field strength, g, and h.
Now, we can find the ratio of the speed at Y to the speed at Z.
Hence, the ratio is 1.29 : 1.